There is no specific du’aa’ to be recited before reading Qur’aan
There is no specific du’aa’ mentioned in the Qur’aan or Sunnah, or in the reliable books of du’aa’s and dhikr, or in the opinions of the reputable scholars, that is to be recited before reading or memorizing Qur’aan. Rather what is prescribed is to seek refuge with Allaah from the accursed Shaytaan before reading, because Allaah says (interpretation of the meaning):
“So when you want to recite the Qur’aan, seek refuge with Allaah from Shaytaan (Satan), the outcast (the cursed one)”
If a person makes du’aa’ at any time, asking Allaah to make it easy for him to memorize Qur’aan or to enable him to understand what he has learned by heart, or any appropriate du’aa’ that he wants to say, without adhering to a particular time for reciting this du’aa’, then there is nothing wrong with that.
With regard to the obligation of having wudoo’ before touching the Qur’aan, you will find the answer to this question under question no. 10672.
It is not necessary to cover the parts of the body that you cover in prayer in order to read Qur’aan, so it is o.k. to read Qur’aan wearing regular clothes, without covering the head.
Shaykh Ibn ‘Uthaymeen said in his discussion on sujood al-tilaawah (prostration required when reading certain aayahs of the Qur’aan): “Sujood al-tilaawah should be done as soon as one reads it in the Qur’aan, so it is o.k. to do sujood in any condition, even bareheaded etc., because this prostration does not come under the same rulings as prayer.” (1/249)
From his words it may be understood that there is nothing wrong with a woman reading Qur’aan with her head uncovered, because she will only read an aayah where a prostration is required when she is reading Qur’aan, so she will be reading it with her head uncovered. The Shaykh did not explain to us whether her head may be uncovered when reading Qur’aan.
We advise you to strive to venerate and respect the Qur’aan, and read it with care, focusing on the meanings, at any time and in any circumstances, whatever is easy for you. The fuqaha’ stated that it is o.k. to read Qur’aan in all circumstances, standing or sitting, sitting cross-legged or otherwise, lying down, riding or walking, because of the hadeeth of ‘Aa’ishah (may Allaah be pleased with her) who said: “The Prophet (peace and blessings of Allaah be upon him) used to lie down with his head in my lap when I was menstruating, and he would recite Qur’aan.” Narrated by al-Bukhaari, 297; Muslim, 301.